The definition of a circle guarantees that the measure of each radius (the distance from the circle's center to a point on the circle) is constant for a given circle. So if we want segments that are the same length, we can always rely on the radii of a circle to construct them.

AP, BP, CP, and DP are all radii of circle P; therefore, they all have the same length.

Construct another circle that has its center on the first circle and that intersects the first circle's center.

c.

Draw segments between the centers of the circles and from each center to one of the points where the circles intersect.

d.

What kind of triangle have you formed? How do you know?

Problem C4

Use Geometer's Sketchpad to create a triangle that is isosceles but not equilateral. How did you do it?

Video SegmentIn this video segment, participants describe their strategies for creating triangles that are isosceles but not equilateral. Watch this segment after you have completed Problem C4 and compare your strategy with those of the onscreen participants.

What was Heidi's strategy for creating the triangle? What was Tom's strategy? How did Catalina prove that Tom's triangle was indeed isosceles?

If you are using a VCR, you can find this segment on the session video approximately 16 minutes and 11 seconds after the Annenberg Media logo.

Problem C5

A rhombus is a quadrilateral with all four sides equal. Use Geometer's Sketchpad to construct a rhombus. How did you do it?